Question

4. (08.02 MC)

Factor completely 2x3 + 10x2 + 14x + 70. (5 points)

(2x^2 + 14)(x + 5)
(x^2 + 7)(2x + 10)
2(x^3 + 5x2 + 7x + 35)
2[(x^2 + 7)(x + 5)]

Answer 1

The answer is D. 2[(x2 + 7)(x + 5)]

Explanation:

Answer 2

2[(x^2 + 7)(x + 5)]

Explanation:

Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...

2x3+10x2+14x+70=

2(x3+5x2+7x+35)

2((x3+5x2)+(7x+35))

2(x2(x+5)+7(x+5))

2(x2+7)(x+5)